Q: The budget constraint $p_1x_1 + p_2x_2 = m$ can be rewritten in terms of $x_2$ as:

$x_2 = \\frac{m - p_1x_1}{p_2}$

Q: Suppose a consumer faces the budget constraint $p_1x_1 + p_2x_2 = m$ and has a utility function $u(x_1, x_2) = x_1x_2$. What is the condition for optimal consumption?

$\\frac{p_1}{p_2} = \\frac{x_2}{x_1}$

Question 1

Which of the following is NOT one of the four elements of a consumer model as described in microeconomics?

Accepted Answer

Production function

Question 2

Suppose a consumer faces the budget constraint $p_1x_1 + p_2x_2 \leq m$. If $p_1$ increases while $m$ and $p_2$ remain constant, what happens to the consumer's feasible set?

Accepted Answer

It shrinks

Question 3

Which property of consumer preferences is illustrated by the statement: 'If $A \succ B$ and $B \succ C$, then $A \succ C$'?

Accepted Answer

Transitivity

Question 4

Given the utility function $u(x_1, x_2) = x_1 + 2x_2$, what is the marginal rate of substitution (MRS) between $x_1$ and $x_2$?

Accepted Answer

$MRS = 1/2$

Question 5

If a consumer's utility function is $u(x_1, x_2) = x_1x_2$, and their budget constraint is $2x_1 + 4x_2 = 24$, what is the optimal bundle $(x_1^*, x_2^*)$?

Accepted Answer

$(x_1^*, x_2^*) = (6, 3)$

Question 6

Which of the following statements about indifference curves is TRUE?

Accepted Answer

Indifference curves are downward sloping and convex to the origin

Question 7

A utility function $u(x_1, x_2)$ is said to be monotonic if:

Accepted Answer

Increasing $x_1$ or $x_2$ always increases utility

Question 8

If a consumer has a Cobb-Douglas utility function $u(x_1, x_2) = x_1^{0.5}x_2^{0.5}$ and faces prices $p_1 = 2$, $p_2 = 4$, and income $m = 24$, what is the optimal consumption of $x_1$?

Accepted Answer

$x_1^* = 6$

Question 9

Which of the following is a valid interpretation of the concept of 'utility' in microeconomics?

Accepted Answer

Utility is a numerical representation of consumer satisfaction

Question 10

Suppose a consumer's preferences are represented by the utility function $u(x_1, x_2) = x_1 + x_2$. If the consumer chooses $(x_1, x_2) = (3, 5)$, what is their utility?

Accepted Answer

$u = 8$

Question 11

Which axiom of consumer theory ensures that a consumer can always compare any two bundles of goods?

Accepted Answer

Completeness

Question 12

If a consumer's utility function is $u(x_1, x_2) = x_1^2 + x_2^2$, which of the following bundles $(x_1, x_2)$ gives the highest utility?

Accepted Answer

$(2, 3)$

Question 13

The budget constraint $p_1x_1 + p_2x_2 = m$ can be rewritten in terms of $x_2$ as:

Accepted Answer

$x_2 = \frac{m - p_1x_1}{p_2}$

Question 14

Which of the following is NOT a property of a utility function that represents rational preferences?

Accepted Answer

Intersection of indifference curves

Question 15

If a consumer's utility function is $u(x_1, x_2) = \min\{x_1, x_2\}$, what type of goods does this utility function represent?

Accepted Answer

Perfect complements

Question 16

Suppose a consumer faces the budget constraint $p_1x_1 + p_2x_2 = m$ and has a utility function $u(x_1, x_2) = x_1x_2$. What is the condition for optimal consumption?

Accepted Answer

$\frac{p_1}{p_2} = \frac{x_2}{x_1}$

Question 17

Which of the following statements about the expenditure function $e(p_1, p_2, u)$ is correct?

Accepted Answer

It gives the minimum expenditure needed to achieve utility $u$ at prices $p_1$ and $p_2$

Question 18

If a consumer's utility function is $u(x_1, x_2) = x_1 + x_2$, and prices are $p_1 = 1$, $p_2 = 2$, with income $m = 10$, what is the optimal bundle?

Accepted Answer

$(x_1^*, x_2^*) = (0, 5)$

Question 19

Which of the following is a consequence of the convexity of preferences?

Accepted Answer

Consumers prefer averages to extremes

Consumer Theory in Microeconomics: Foundations and Applications

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